A study of young children was designed to increase their intake of whole-grain, rather than regular-grain, snacks. At the end of the study, the 79 children who participated in the study were presented with a choice between a regular-grain snack and a whole-grain alternative. The whole-grain alternative was chosen by 55 children. You want to examine the possibility that the children are equally likely to choose each type of snack. H0:p=0.5 Ha:p≠0.5 Perform the significance test. (Use α=0.01. Round your test statistic to two decimal places and your P-value to four decimal places.)

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A study of young children was designed to increase their intake of whole-grain, rather than regular-grain, snacks. At the end of the study, the 79 children who participated in the study were presented with a choice between a regular-grain snack and a whole-grain alternative. The whole-grain alternative was chosen by 55 children. You want to examine the possibility that the children are equally likely to choose each type of snack.  H0:p=0.5  Ha:p≠0.5  Perform the significance test. (Use α=0.01. Round your test statistic to two decimal places and your P-value to four decimal places.)

rogreenhoxa8 · Accepted Answer

Step 1 Given Information No of children participated (n)=79 No of children chosen (x)=55 p^=xn=5579=0.696 Null and alternative Hypothesis Null Hypothesis: p=0.5 Alternative Hypothesis: p≠0.5 Test statistic z=p^−pp(1−p)n=0.696−0.50.5×(1−0.5)79=3.48 Step 2 p-value p−value=2xP(Z&amp;gt;3.48)=2x(1–P(Z&amp;lt;3.48))=2x(1–0.999748)=0.000501 P(Z&amp;lt;3.48)=0.999748 (Using Excel function=NORM.S.DIST(B 20, TRUE) p−value&amp;lt;0.01, So, reject null hypothesis and conclude that children are not equally likely to choose each type of snack.

A study of young children was designed to increase their intake of whole-grain, rather than...

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